You can analyze the circuit shown in figure 4 easily if you followed my previous posts. But here we are about to talk something special on this circuit.
Consider the current goes through the resistor ‘r’ is zero. This means that the voltage difference between ‘r’ is zero. (If you are not familiar with these things, please refer my previous posts regarding ohms low, KCL & star delta transformation)
VBD = 0
Therefore we can see that the voltage between the resistor R4 and R2 must be equal.
By voltage dividing method (or you can simply use the ohms low on each branch)
VDC = (V x R4 ) / (R3 + R4) ---(1)
VBC = (V x R2) / (R1 + R2) ----(2)
But we know that VDC = 0
VDC = VBC
R4 / (R3 + R4) = R2 / (R1 + R2)
(R3 + R4) /R4 = (R1 + R2) / R2
1 + (R3/R4) = 1 + (R1/R2)
(R3/R4) = (R1/R2)
(R1/R3) = (R2/R4)
So If the above equations are true for any bridge circuit, we can say that the voltage difference between D & C is zero and therefore there is no use of the resistor ‘r’. Then we can redraw the circuit as shown in figure 17.2.
This kind of circuits are called Wien bridges. This is an important point. There are so many uses of this Wien bridge method.